Will the Dodgers pursue Zack Greinke?

They look pretty set, don’t they? The Dodgers did most of their off-season shopping midseason, those early birds.

If you assume Matt Kemp and Carl Crawford will be fully recovered from surgery to start next season – and at this point, the Dodgers have all fingers crossed – then the lineup is already filled out. Only role players need apply.

General Manager Ned Colletti talked about re-signing his three free agents in the bullpen – Brandon League, Jamey Wright and Randy Choate – and if he does, then the bullpen looks solid and deep.

That leaves the rotation, which at first blush looks booked too. Clayton Kershaw, Chad Billingsley, Josh Beckett, Ted Lilly, Chris Capuano and Aaron Harang would actually leave the Dodgers with an extra starter.

But Lilly, who will be 37 in January, is coming off arthroscopic shoulder surgery. After an excellent start (5-0, 1.79 ERA) Lilly never pitched again after his shoulder flared up May 23.

And the Dodgers won’t know if Billingsley will require Tommy John surgery until the middle of next month. Even then if he avoids surgery, can you really count on him being healthy all year?

“We’ll have to be cautious with it and have to prepare really not knowing. It’s not just necessarily Chad. Who knew a year ago that Chad would have an issue? You always want to continue to strengthen your pitching.”

So the one thing the Dodgers are expected to pursue is another starter. They already have an ace in Kershaw, but lack a clear No. 2 guy, someone to really complement their star left-hander.

“I would say a starting pitcher is what we’re seriously going to have to look at,” Colletti said. “We don’t know what we’re going to get from either players who are either recuperating right now or looking at surgery. We can’t wait until we find out something that you can’t adjust to.”

The market is not exactly overflowing with major prospects, either. The only top-flight pitcher expected to declare free agency is Zack Greinke. He is coming off a four-year, $38-million contract. He reportedly turned down a five-year, $100-million deal from the Brewers before they traded him to the Angels. And it’s not like the Angels won’t be looking for pitching.

The Dodgers’ payroll has expanded so rapidly since Guggenheim took over the club, you might logically think they’ve reached the end of the splashy moves. Traditional logic, however, has taken a flight to Pluto since Guggenheim arrived.

Mark Walter, the team’s controlling partner, said they are still willing to spend on the right player. He did, however, express reservations about shelling out major dollars for a pitcher.

“Pitchers break,” Walter said.

If the Dodgers determine it’s unwise to pursue Greinke, then adding another starting pitcher would take them into the trade market. And then it’s everyone into the water. They could make another run at Cliff Lee or Beckett’s former teammate Jon Lester.

They could try a lot of things in the trade market, which doesn’t mean any would come to fruition. Which could yet, if reluctantly, turn them back to Greinke.